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inequality with abc=1

Source: Serbia & Montenegro ST 2005 problem 5; Baltic Way 2005/5

June 1, 2005
inequalitieslogarithmsinequalities proposed

Problem Statement

Let aa, bb, cc be positive real numbers such that abc=1abc=1. Prove that aa2+2+bb2+2+cc2+2≤1\frac a{a^{2}+2}+\frac b{b^{2}+2}+\frac c{c^{2}+2}\leq 1
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